Credit Risk

Credit risk is the possibility of incurring a loss in profits or capital due to a default on a loan. The default may be due to either the loan principal or the interest – or both – not being repaid at maturity.

Financial institutions which grant their clients credit, such as banks, credit card companies, bond purchasers, etc., are all exposed to credit risk.

The subprime crisis in the United States was the result of materialized credit risk. The processes leading up to the crisis, the dramatic events of the crisis itself, the recovery period and the financial reality in its wake are all fascinating topics in their own right, but this book is too short to explore them all in detail. We will nevertheless state that the crisis was triggered when, at one point, it was discovered that borrowers who had taken credit from the banks as mortgage were unable to repay it according to the agreed terms. This phenomenon was so widespread that the banks themselves incurred severe losses, with some even driven to bankruptcy. The crisis then spread to other sectors of the American economy as well as to other parts of the globe.

In order to mitigate credit risk, we must first properly define it. It turns out that between full repayment of the loan according to its terms and complete non-repayment, there is a wide range of definitions for bad debt.

Borrowers who fail to meet the terms of a loan are called `bad borrowers` and the debt they owe may be divided into the following categories:

- The debt will definitely not be repaid (bad debt).

- There is a slight chance that the debt will be repaid (doubtful debt).

- The debt will probably be repaid, but there will be a delay of at least 90 days (non-performing debt).

- The debt will be repaid but there are issues at the moment, such as liquidity problems (debt in temporary arrears).

- The principal will be repaid but not the interest (non-profit debt).

Different states and regulators classify borrowers using different systems, and any further exploration of the topic therefore requires that the regulations of each individual country be discussed separately.

It is important to classify bad borrowers, as each type requires different mitigation. For instance, bad debt is registered as a loss on the income statement, whereas a debt in temporary arrears will affect a bank’s cash flow but has almost no effect on its income statement.

The field of credit risk management features many important concepts. Among these are credit exposure, counterparty credit risk, credit valuation adjustment, etc. In this section we shall focus on the most important of these:

Probability of Default (PD)

PD is the probability that a default (i.e., a failure to return credit) will occur. This event of default is defined in a binary manner – either a default occurred or it did not. For this reason, the precise definition of “default” is of critical importance. At one end of the scale, default may be defined as the conclusion of a legal process and a declaration of bankruptcy by the borrower, who is consequently unable to return the credit; at the other extreme, default may be defined as a delay in delivering just a single partial payment out of several.

For instance, if a company whose bonds are traded at the bond market is late in paying its coupons, even by one day – the company is considered to have defaulted. On the other hand, many banks allow their clients up to 90 days of arrears before determining that the client has defaulted.

PD is measured in percent. For instance, if PD=0.5%, this means the borrower has a 0.5% probability of defaulting in the coming year. The value 1-PD is the rate at which loans will be returned (sometimes referred to as the “survival rate” of the borrower). In this example, there is a probability of 99.5% that the borrower will repay the loan in accordance with the terms agreed upon when the loan was granted.

The PD value affects the income of the creditor. If PD is zero (a hypothetical situation where failure is impossible) the rate of returned loans (or borrower’s “survival rate”) will be 100%, and the credit giver will enjoy a profit of the interest amount of money given as credit. A positive PD means a lower repayment rate and consequently reduced income and profits.

PD values may be divided into categories such as those of Standard & Poor’s Rating Services for business firms. Each rating group is assigned upper and lower default rates on an annual basis. For instance, firms with a PD of up to 0.14% will be rated A. Firms with a PD between 1.35% and 14.65% will be rated B.

A risk manager, upon being informed that a company has been rated A, must at the very least check who has given it this rating, when it was rated and what its PD value is in order to properly assess its credit risk.

The chart shows the PD values for the rating categories BBB- and BB+ as well as a general average, for the years 1981-2014. Three peaks may be observed, in 1991, 2001 and 2009, indicating that in these years, companies with a BB+ rating maintained their rating, despite the fact that their probability of default had more than doubled compared to other years during this time frame.

These changes are connected to other financial developments:

The Gulf War broke out in 1990, and the price of an oil barrel doubled, from USD 30 to USD 60. Although this change had little effect on the S&P500 index, it did significantly increase the probability of default for many companies.

The year 2000 saw a stock crisis in the wake of the dot-com crash. Many companies went bankrupt the following year, affecting the rating system.

The subprime crisis of 2007-2008 led to a readjustment of ratings the following year, to correspond with the increased probability of default at the time.

While adjusting the rating system to different PD rates may be seen as an expression of flexibility and understanding with regards to the effects of business cycles, it has also been the source of some criticism, as it is difficult to measure the risk of a company if the scale changes with such frequency.

Nevertheless, this system is very widespread, and it is a convenient method which allows us to distinguish between companies with high and low credit risk.

Exposure at Default (EAD)

EAD is the credit exposure in the event of default, measured in monetary terms. For example, a borrower owes ISK 100,000 to the Icelandic bank Íslandsbanki. It turns out, however, that this borrower is broke and will not be able to repay the bank. The bank’s credit exposure toward this borrower is ISK 100,000.

The size of a loan with monthly repayments decreases over time. At first, the money being repaid mostly covers the interest rather than the principal. Over time, however, the portion covering the principal gradually increases and the portion assigned to the interest decreases, until the loan is eliminated altogether. For such a loan, EAD goes down every month as a function of time.

EAD generally depends not only on time but also on the type of loan, its accounting value and any mitigating factor which might affect credit risk (e.g., execution of surety bonds).

The precise manner in which EAD is calculated varies by regulator, and in some cases even by individual banks, which may fall under the jurisdiction of the same regulator but use different methods for managing credit risk.

Risk managers who specialize in managing credit risk must be familiar with the various types of calculations in general, and in particular the specific instructions required by the regulations under which they operate.

Loss Given Default (LGD)

LGD is the monetary loss in the event of default, measured as percentage out of the total credit exposure in case of failure. Suppose a borrower owes Íslandsbanki ISK 100,000, but is bankrupt and therefore unable to repay the debt. However, the bank can realize the borrower’s collateral and recover ISK 60,000, reducing the bank’s loss to just ISK 40,000, i.e., LGD in this case would be 40%.

The recoverable part of the loan in the example above is 60%. This is often referred to as the recovery rate and equals 1-LGD.

The ability of the lender to recover at least a part of the loan is affected by various factors, including but not limited to the following:

Position on the creditor list. Generally speaking, the higher a creditor’s place on the list, the higher their recovery rate, i.e., they will recover a greater portion of the loan and will enjoy a lower LGD compared to other creditors.

Liquidation costs. A factory which has declared bankruptcy will often own equipment worth hundreds of thousands of U.S. Dollars and, on occasion, will also hold bank deposits, tradable stocks and other forms of property which may be liquidated in order to eliminate a portion of the debt.

Deposits and stocks are relatively easy to liquidate, and the money received from their sale may be used to cover the debt. The liquidation of types of property, however, is often a more complicated process, and the search for a buyer often entails additional costs. Furthermore, liquidation in the wake of bankruptcy often results in a forced sale, leaving the creditors with little bargaining room and compelling them to sell at lower prices than they would have succeeded in obtaining under different circumstances. As a rule, the easier it is to liquidate a company’s property, the higher the recovery rate and the lower the LGD.

Geographical spread. When the property is scattered across distant areas or even countries, it is often more difficult to sell. Sometimes, the same type of property (e.g., real estate) may be sold with greater ease in one country than in another, due to differences in national legislation, etc. As a rule, the smaller the geographical spread, the higher the recovery rate and the lower the LGD.

Length of recovery period. Stocks may be sold fairly quickly, whereas selling factory buildings might require some time. During this time, the debt continues to accumulate and the interest continues to accrue. A shorter recovery period signifies a higher recovery rate and a lower LGD.

Collateral

One way to ensure a low LGD and a high recovery rate is by pledging assets as collateral.

Collateral is the borrower’s pledge of a particular asset or group of assets to guarantee the repayment of a loan. For example, borrowers who take out a mortgage pledge their house or apartment as collateral to the bank. Should the mortgage not be repaid, the bank may repossess the apartment and attempt to sell it in order to recover the unpaid debt.

Many forms of collateral exist:

Equity (weighed against liabilities)

Deposits, savings plans, tradable securities

Future obligations (postdated checks, contracts)

Real estate

Supplies and equipment

Personal assets of the owners

It is important to continuously reevaluate the collateral throughout the loan’s lifetime. For example, the value of tradable securities may change on a daily basis. It is certainly conceivable that the value of such securities may drop below the value of the loan itself. For this reason, changes in the value of the assets used as collateral must be constantly monitored.

Collateral has a substantial impact on LGD. Collateral which covers the full extent of a loan can greatly reduce LGD and ensure a recovery rate of almost 100%.

Collateral which is not sufficient to cover the full extent of the loan will not reduce LGD. Such a situation may occur for various reasons, most often in cases where the collateral was not properly evaluated to begin with, or its value has dropped since the loan was taken out.

Financial institutions which grant their clients credit must dedicate resources to the re-evaluation and management of collateral in order to maintain high recovery rates for all the lines of credit they offer. While collateral is a tool for managing credit risk, financial institutions must also manage the risk embodied in the collateral itself.

M

The term to maturity, M, is the time left until the loan must be repaid, measured in years. To give an example, let us return to the example of the Icelandic bank and suppose there is a borrower whose credit matures in six months. In this case, M would be 0.5.

Time is a vital factor in all the parameters we have reviewed so far – PD, LGD and EAD. For instance, a company’s PD at the start of a year is not the same as its PD at the end of that year. For this reason, estimates of credit risk which factor in PD, LGD and EAD must relate to a specific value of M.

For one year, M equals 1. For half a year, M=0.5. How is M calculated for a period of 45 days?

It turns out that the calculation of M for non-whole terms is not as simple as it might first seem. One may calculate the ratio of 45 days from 365, 0.123288. However, what happens during a leap year? In such a case the year will be 366 days long, and the ratio will change to 45 from 366, i.e., 0.122951. To a reader unaware of the enormous sums of money concerned, a difference of 0.000337 might seem negligible. However, even for a bank with a loan balance of one billion U.S. Dollars (a modest balance in banking terms), this difference represents USD 336,000 per year… For the ICBC (Industrial and Commercial Bank of China Limited), whose credit balance is USD 1.8 trillion, this seemingly negligible difference will amount to USD 337 million every year.

The effect of time on financial calculations is substantial. The International Swaps and Derivatives Association (ISDA), which assists in the international regulation of financial derivatives trading, has issued guidelines regarding the manner in which the time element is to be calculated.

The same time calculations must be employed when assessing credit risk and when referring to the loan for which the risk assessment is being conducted. In fact, it is necessary to examine each loan on an individual basis and calculate its credit risk separately. This typically involves large volumes of information and requires extensive computing capabilities (in both software and hardware).

Expected Loss (EL)

EL is an estimate of the loss which could result from a failure to repay credit, and it is measured in terms of monetary value. Assuming information regarding the main components of credit risk is available, it is possible to calculate EL as soon as a loan is issued. Let us explain; where credit is concerned, there are two possible outcomes at maturity:

The normal outcome, where the borrower has repaid both the loan and the interest in full. In this case, the loss will be 0. The probability of a normal outcome is 1-PD.

A case of default, where the borrower does not repay the loan according to the agreed-upon terms. In this case the loss will be EAD x LGD. The probability of such a failure event occurring is PD.

The time-adjusted (M) expected loss is calculated using the following formula:

EL(M) = [1- PD(M)] x 0 + EAD(M) x LGD(M) x PD(M)

As the first part of the formula equals zero, the formula may effectively be written thus:

EL(M) = EAD(M) x LGD(M) x PD(M)

To give an example, let us calculate EL for a borrower with the following data for the coming year:

Mortgage: EUR 100,000

Repaid thus far: EUR 20,000

Current house value (as collateral): EUR 70,000

Cost of house sale: €10,000

Failure rate for mortgages: 40%

Calculating EAD: The exposure is EUR 80,000 (EUR 100,000 mortgage minus EUR 20,000 already repaid).

Calculating LGD: LGD is 25% (house value of EUR 70,000 less the EUR 10,000 cost of selling the house equals EUR 60,000 in total. The recovery rate is therefore 1-LGD, i.e., 75%, or EUR 60,000 out of EUR 80,000).

PD is a given, in this case 40%.

EL may now be calculated as follows: EUR 80,000 x 25% x 40% = EUR 8,000.

Measurement

In order to measure credit risk, we must first calculate each of the main risk components separately.

There may be some complications involved in calculating EAD, LGD, EL and M, but it is a relatively straightforward process of addition, multiplication and division. These calculations are determined by local regulations dictating which lines in the balance sheet must be included and in what capacity. These regulations vary from country to country.

Calculating PD is a different matter altogether. The main PD estimates used are:

Scoring (score card, Altman’s Z-score)

The scoring method for calculating the probability of default makes use of a questionnaire where each answer is assigned a different score. For instance, a borrower younger than 22 years old will be awarded 100 points, between 22 and 26 years of age 120 points and so on. A borrower older than 42 will be awarded the greatest number of points possible, 250.

A borrower who owns an apartment will get 225 points, but one who rents an apartment will only get 110 points.

A borrower with an income of less than USD 1,000 will only receive 120 points, but an income of over USD 58,000 will earn the borrower 260 points.

The questionnaire is completed in this manner, and at the end all the points are summed up. If the total sum is higher than a set minimum value, e.g., 600, the applicant will be granted a loan. Otherwise, the loan will not be approved.

For example, a borrower has requested a loan for a sum of USD 100,000. She is 35 years old; her income is USD 38,000 and she owns a house. Should the bank approve her request?

In this case, the answer is yes, as according to the table her score is 660, above the minimum required score of 600.

The scoring method’s primary strength is its simplicity. However, it can only return a binary yes/no answer. For instance, it is quite possible that we would agree to give credit to a potential borrower with a score of 580, but for a smaller sum of money and with a higher interest rate to make up for the greater risk. To make this possible the questionnaire must contain a large number of scoring categories, negating the initial simplicity of the method…

This method is widely employed by financial institutions which provide large numbers of relatively small loans (typically to individual borrowers).

Altman’s Z-score

Altman’s scoring method is primarily used to classify firms into three categories: low risk, medium risk and high risk of bankruptcy.

Using this simple model, a number of financial ratios are multiplied, each by a different coefficient, and then summed up to give a final score.

The financial ratios are:

X1=working capital / total assets

X2=retained earnings / total assets

X3= Earnings before interest and taxes (EBIT) / total assets

X4=market value of equity / book value of liabilities

X5=sales / total assets

The results of these ratios are then assigned to the following formula:

Z = 1.2X1+1.4X2+3.3X3+0.6X4+0.99X5

Z is greater than 2.99 – low risk of bankruptcy (“safe zone”).

Z is between 1.81 and 2.99 – medium risk of bankruptcy (“gray zone”).

Z is lower than 1.81 – high risk of bankruptcy (“distress zone”).

Example:

Is a company with the following data at risk of bankruptcy?

170,000 Working capital

670,000 Total assets

60,000 EBIT

2,200,000 Sales

380,000 Market value of equity

240,000 Book value of liabilities

300,000 Retained earnings

Let us now calculate the financial ratios:

X1= 0.2537

X2= 0.4478

X3= 0.0896

X4= 1.5833

X5= 3.2836

This will result in the following formula:

1.2×0.2537 + 1.4×0.4478 + 3.3×0.0896 + 0.6×1.5833 + 0.99×3.2836 = 5.43

5.43 is greater than 2.99, i.e., the company is in the safe zone.

The Z-score’s strength lies in its simplicity as well as its ability to divide companies into intermediate classes in addition to the main three. However, this method is mostly used for businesses and is not suited to rating individual borrowers.

Profiling Methods

Profiling is the calculation of bankruptcy rates for groups of borrowers. For instance, we may identify a group of borrowers who match certain criteria, e.g., real estate borrowers (industry sector) selling real estate for construction (product) in France (geographical area) who are private contractors (type of entity). We then proceed to check how many cases of default occurred for all the borrowers in this group, giving us its PD value.

Profiling allows for greater precision than the two methods previously discussed. Furthermore, it may be applied to both corporate borrowers and individual borrowers, and even to borrowers in the public sector, etc. However, the precision of this method drops sharply when smaller groups are examined. For instance, if a category contains only ten borrowers, none of whom have ever defaulted, this will give us a PD of 0%... This is indeed the nominal value, but its statistical significance is somewhat questionable.

Profiling is an accepted method for banking systems where millions of borrowers take out hundreds of millions of loans, and the values provided by this method are statistically valid.

Credit VaR

The VaR method allows us to estimate the expected loss for a given period of time at a given level of statistical significance. For instance, credit VaR of JPY 30 million, for a period of 100 days, at a probability of 99%, means that we may expect to see a credit failure in excess of JPY 30 million on one day out of the coming 100 days.

Credit VaR may be calculated either for the total credit portfolio, or separately for specific rating categories for a particular time horizon.

This method offers considerable advantages in measuring credit risk and breaking down the structure of credit risk over time (credit risk term structure).

The main strength of this method is its great flexibility in calculating credit risk for varying time ranges and rates of risk. Its weakness is its technical complexity.

Merton’s option pricing model

According to Merton’s option pricing model, the probability of default depends on the market price at which a share is traded.

The premise at the core of this model is that the value of a company is the difference between its assets and its liabilities. If this value is negative, the company’s value is assumed to be zero.

In this model, the x-axis represents the company’s value and the y-axis represents its share price. The red line on the graph marks the correlation between these two values. Up to the debt level marked D, the company’s value is zero. From this point onwards, company value and share price are directly correlated.

The formal framing of Merton’s model resembles the pricing of an option on a base asset, V, where the exercise price of the option is D. As the option value approaches 0, the company draws ever nearer to failure. If the value of the option is close to V, the company is solvent.

Merton’s model is relatively easy to apply to companies whose shares are traded in the stock market.

Another options pricing model worth mentioning is the KMV model, which is a development of Merton’s model with a number of added parameters and simplifying assumptions, permitting more accurate prediction of a company’s credit risk.

The strength of both the Merton model and the KMV model is the simplicity and ease with which they allow us to measure risk (despite their apparent mathematical complexity…). Some would argue, however, that these models are flawed as they rely on historical market prices, which may be affected by unrelated economic factors. Their greatest weakness, however, is that they cannot be applied to individual borrowers or to companies which do not issue shares to the public.

Binary regression

Binary regression is a statistical model which allows us to measure the probability that one out of two outcomes will occur, given one or more explanatory variables. With regards to credit risk, the possible outcomes are:

1 – A credit failure event occurred.

0 – A credit failure event did not occur.

For instance, using binary regression it is possible to measure with great precision the probability of a failure event if the borrower is 40 years old, holds a senior position at a medium-sized real estate company, is married with two children and has no prior liabilities.

The two most widely used approaches use the models Logit and Probit, which differ in the form of statistical distribution each model assumes.

Binary regression is capable of grouping together all borrowers (reliable and risky alike) using a single model and measuring the probability of default for each one. This means a more precise measurement of credit risk may be assigned to each borrower. However, this approach requires extensive historical data, including on historical default events, and this is not always available.

Stress testing, scenarios and sensitivity testing

Stress, scenario and sensitivity tests may also be applied to credit risk. The purpose of these tests is to estimate the credit risk under exceptional circumstances, e.g., what would be the expected loss if the credit ratings of all current loans were to drop by one level all of a sudden – e.g., how would EL be affected if every single firm rated AA were demoted to a rating of A.

Credit risk management

Now that we understand what the components of credit risk are and how they are measured, how do we actually manage credit risk?

Suppose we are an institution which gives out loans, and we have been approached by the owner of a hypsometrical company named Grass Fragrance ltd., which produces and markets garden furniture. The owner wishes to obtain a loan of CAD 150,000 for a period of ten years. Let us also assume that we have measured a PD of 2.5% for the company. What should we do next?

In the risk management process, we are now at the stage of “monitoring and assessing risk” (see introduction). However, measuring PD alone is not sufficient for this purpose. We must also measure the expected loss (EL):

As the loan has not yet been granted, EAD is CAD 150,000. Assuming no collateral has been pledged, EL for one year will be CAD 3,750 (150,000 x 100% x 100% x 2.5%).

Money-lending and credit providing institutions are typically risk averse and reluctant to support adventurous enterprises. They will therefore only approve the loan if its EL is lower than the greatest loss they are prepared to incur. For instance, if the annual interest rate on this loan is 7% (giving an expected profit of CAD 10,500 for the first year), and it covers operational costs and other risks as well, such an institution will be willing to approve the loan to Grass Fragrance LTD.

However, an interest rate below 2.5% would imply a risk greater than the expected loss, and the loan would be denied.

How can we reduce the risk?

The risk may be reduced through the process risk management, following the methods described in the introduction of this book:

Risk avoidance. The option of denying the loan altogether is perfectly reasonable from the standpoint of management. We may choose to deny Grass Fragrance the loan, thus avoiding the potential loss. This method reduces credit risk by reducing the exposure to the risk factor.

Risk reduction procedures. The financial institution may demand that Grass Fragrance pledge collateral as a guarantee in case of failure.

It is also possible to approve the loan, but only grant a more limited sum of money (e.g., CAD 50,000).

Risk transfer. For certain types of loans, such as mortgages, banks require that the borrower possess a life insurance policy. Thus, if the borrower were to pass away unexpectedly, the insurance company would still have to repay the bank.

The most frequently employed method for managing credit risk is by charging higher interest rates from riskier borrowers. This means that those risky borrowers who do fulfill their obligations effectively subsidize those who fail to do so. Thus, the creditor creates a mechanism where the credit risk is transferred collectively to all the borrowers belonging to a particular risk group.

Acceptance of consequences. This is one of the commonest methods in bond investment. A bond is a financial tool which allows investors to grant a loan to a business. Occasionally the business defaults on its obligations to the bond owners. An investment in bonds is conducted according to the bond’s risk rating and requires an analysis of the potential risks and rewards. Although they may not readily admit this, investors accept a potential loss in the event of credit failure. For example, when we invest USD 10,000 in the Italian government, we accept the fact that we may end up losing a part of our investment.

Recovery plan. Collection of an unpaid debt constitutes the recovery process for a credit failure. Various aspects of the debt collection process must be planned in advance in order for it to succeed. For instance, any legal issues which may arise when we attempt to collect the debt (due to changes in the ownership of the collateral or an inability to realize the collateral as a result of laws which prevent us from doing so) must be resolved. It is also essential to allocate the manpower required for executing the debt collection. Occasionally a financial investment is required in order to obtain the necessary documents or legal counsel in order to recover the debt, and so on. In addition, many financial institutions are required to allocate a certain minimal capital reserve which will allow them to recover even from rare instances when materialized credit risk results in exceptionally severe losses.

Another method for reducing credit risk combines the possibility of reducing damage with the option of transferring it to another party, using a financial tool called Credit Default Swaps (CDS).

CDS is a tool for hedging credit risk, which provides protection against failure to repay a debt. In such an event, CDS buyers reserve the right to sell their bonds at a stated value.

The annual sum paid in exchange for this protection is called the CDS spread, and it also serves as a measure of the perceived credit risk in the market. A higher spread implies greater risk perception. This measure makes it possible to track developments in the market over time (a wider and narrower spread correspond to higher and lower risk perception respectively), as well as compare the credit risk of various financial institutions.